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16 January, 22:50

If the absolute temperature of a gas is quadrupled, what happens to the root-mean-square speed of the molecules?

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  1. 17 January, 01:02
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    The root-mean-square speed measures the average speed of the gas molecules. The relation of root-mean-square speed and the absolute temperature is based on the kinetic molecular theory of gases.

    The root-mean-square speed define as ν_rms

    where:

    ν_rms = √ (3RT/M)

    R = universal gas constant; 0.8206 L-atm/mol-K

    T = absolute temperature

    M = molecular weight of gas particles

    So, if the temperature of the gas is quadrupled the root-mean-square speed will be doubled.

    Proof:

    Since T is quadrupled, then T=4T

    Substitute to the formula of root-mean-square speed,

    ν_rms = √[3R (4T) / M]

    = 2√ (3RT/M) since the square root of 4 is 2

    Therefore, root-mean-square speed is doubled when the absolute temperature is quadrupled.
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